The continuing goal of this multifaceted project is to develop and employ mathematical and physics-based methodologies which can be used to investigate complex biological structures and materials. One example from this reporting period is a collaborative project to provide the basis for quantitative assessment of the chemotactic response of polymorphonuclear (PMN) leukocytes and other amoeboid cells (carried out with personnel at the National Cancer Institute). Migration of cells along gradients of effector molecules, i.e., chemotaxis, is necessary during immune response and is involved in tissue development and cancer metastasis. The experimental assessment of chemotaxis thus is of high interest. The agarose spot assay is a simple tissue culture system used to detect directed cell movement induced by gradients of diverse materials, such as peptides released from the sites of bacterial infection and macromolecules that serve as growth factors. Direction sensing requires that gradients be appropriately steep, and it is necessary to know how the chemical gradients developed in this assay change over time so proper conditions for measuring chemotaxis can be effected. We have used numerical solution of the Diffusion Equation to determine the chemoattractant gradient produced in the assay. Our analysis shows that, for the usual spot size, the lifetime of the assay is optimized if the chemoattractant concentration in the spot is initially 30 times the dissociation constant of the chemoattractant-receptor bond. This result holds regardless of the properties of the chemoattractant. With this initial concentration, the chemoattractant gradient falls to the minimum threshold for directional sensing at the same time that the concentration drops to the optimal level for detecting gradient direction. This and other results of our analysis provide guidelines for application of this inexpensive and easily implemented method. A manuscript, Improving the design of the agarose spot assay for eukaryotic cell chemotaxis, currently is under review. Related assays also are being analyzed, in conjunction with work directed at obtaining better understanding of the mechanism of cell adhesion and how it affects chemotaxis and other aspects of amoeboid locomotion. Another of our activities involved a study of the effects of pH and sample dehydration on the diffusion of small fluorescent molecules through polymer gels and solutions. This work is part of a continuing effort to understand how the properties of dense polymeric materials affect the movement of embedded molecules and nanoscopic particles. Fluorescence correlation spectroscopy (FCS) was used in this study. A unique power of FCS is that, in principle, it can detect the motions of fluorescent entities while signals from non-fluorescent surroundings can be ignored, even if the surrounding material is optically turbid (S. Zustiak, J. Riley, H. Boukari, A Gandjbakhche, and R. Nossal. J. Biomed. Optics 17:125004, 2012). For this reason, FCS increasingly is used to study particles moving in complex environments, examples being molecules moving on the surfaces of, or within, biological cells. In our recent work we used FCS to measure the translational diffusion coefficient of two fluorescent nanoprobes, rhodamine (R6G) and carboxytetramethylrhodamine (TAMRA), embedded in poly(vinyl alcohol) (PVA) solutions and gels. The diffusion coefficient was measured as a function of the pH and polymer concentration. Exchange experiments showed that the effect of pH on nanoprobe diffusion is reversible. The pH effect is observable even though the PVA chains are partially immobilized. However, interactions do not create permanent bonds between PVA and the fluorophores, as can be inferred from observations which show that R6G or TAMRA nanoprobes can diffuse freely in and out of the gels. As observed previously with other probes (A. Michelman-Ribeiro, F. Horkay, R. Nossal, and H. Boukari. Biomacromolecules 37:10212, 2004), we found that the more concentrated the solution the slower the nanoprobes move. and crosslinking the polymer chains causes the diffusion of the nanoprobes to become even slower. This behavior remains intriguing since the size of the nanoprobes (1.6 nm) is significantly smaller than that of the pores formed by the cross-linking. We also designed and built an optical chamber to determine the diffusion coefficient of PVA solutions and gels subjected to controlled dehydration, and found that dehydration induces a systematic decrease of the diffusion of TAMRA in both solutions and gels. These results demonstrate that transient physical interactions between the nanoprobes and the PVA polymers have a significant effect upon nanoprobe diffusion. Hydrogels are used in many biomedical applications, including the engineering of tissue phantoms, designing extracellular matrices for tissue regeneration, and the development of efficient drug delivery systems. Despite such important medical applications, the sieving properties of gels remain poorly understood. We are using FCS to obtain information necessary to obtain a deeper physical understanding of the complex interactions between probe particles and surrounding matrix. Similar schemes can be developed to study the movement of materials through intact tissues. Based, in part, on our understanding of gel properties, we also developed a multi-well polyacrylamide-based assay to assess how the mechanical properties of the surroundings of cells affect their fate, particlularly as relating to responsiveness to drugs. Polyacrylamide was chosen due to the ease of manipulating its stiffness and the ability to link that material to extracellular-matrix constituents. The gels were coated with collagen and used to test the effect of stiffness on the susceptibility of cancer-derived tissue culture cells to agents that target microtubules.